Place the mouse over the health value displayed in the minipanel for detailed info on this indicator. Also, City Adviser's Overview has a population section that will display health alerts.
Factors taken into account when calculating your population's health state are:
Health increases the amount of free Premium Points (if the chances are high enough) every day!
As its name states, happiness is an indicator of how happy or unhappy your people are. The most detailed information on happiness can be found by placing the mouse over the happiness value in the minipanel.
Short info on happiness can also be found in the City Adviser's Overview screen (under the Population section).
Happiness is calculated based on:
Happiness increases the chances of receiving free Premium Points every day! It also influences the chances for a successful propaganda. When people are disgruntled it's much easier to convince them of certain truths... unless they're your people :)
Growth refers to your population's growth rate. The number of your citizens may be influenced by factors like birth, immigration, death, unhappiness, emigration.
In order for a city-state to grow, it first needs to provide housing to its new citizens. The housing can be extended to each ruler's own liking, there's no imposed value for the housing extension.